Some principles which might apply in any case:
- Bigger armies are easier to find and observe. Which provides an inherent advantage to smaller forces, especially covert ones. Their support structures would be harder to locate and strike against. Operations of the bigger army would be easier to notice and respond to.
- Bigger armies have a fundamental capability of undertaking siege & sweep operations against smaller ones, which smaller armies must at all costs avoid. What level of numerical superiority is needed to surround and sweep a given object, would be a function of the size of the object and the dimensions of movement available. On land, that generally makes two dimensions of movement, and the most efficient formation to surround something is a circle. In space, it generally makes three dimensions, and surrounding something in an easy case takes a sphere. This suggests that the numerical superiority required to perform a siege operation in 3 dimensions is one step bigger than in 2 dimensions. Peculiarities of landscape and (in)ability to use it, as well as deviations of the line of siege from a perfect circle or sphere, would of course count in favour or against the relevant parties, generally favouring the defending or local party, under the assumption that they'd be better adapted to maneuvering in their environment, which might be a pretty small difference in space or air, yet a comparatively big difference on land.
Neither. it is simply to repulse the invaders.
Usually, some kind of priorities end up existing... either as a result of goals/ideology or a byproduct of organizational structure. These in turn shape how the force in question behaves, which shapes how they are perceived by non-involved persons, which determines if their support grows or diminishes... which could well determine if they can continue their course of action (invade, seize control, or oppositely demolish a system of control), or end up falling apart (e.g. defect, either out of disillusionment or to make it off with looted treasure) or end up being overwhelmed by opposition...
...which makes it all more complex, and not a direct function of size.
The popular attitude would be nearly universally against the big army, as the overall societal structure is one of 0 coercion, and they would be attempting to set up a coercive State.
Well, if this assumption would hold, then the bigger army would get denied factual information, which is a serious disadvantage. To overcome a lack of cooperation on new terrain, they would need a qualitatively better technology.
Another question is: to which degree could non-involved population deny information or assistance to one or another force. Basically, the autonomy of the population and their amount of choices would matter. If the invading force makes up 1% of the total population and behaves like an ass, and the population is highly autonomous, has lots of choices and is heavily armed, they'll join the defending force and crush the invading force. If however the armies are comparatively big relative to the non-combatant population, and the latter does not have a high degree of choice available, such a scenario may not be even remotely feasible...
...and thus, more complexity, and fewer simple answers.
Whether a group of persons pursuing some struggle, operating by certain principles and organizing in certain ways... whether they prevail or fail, does not in my opinion depend on their initial size, but rather, whether they gain ability or lose it in the process; whether their ways are efficient or counterproductive... and ultimately, how their behaviour matches their scale, and whether they can adapt it to changes in scale.
From my viewpoint, it is thus rather hard to associate a given initial size with a probability of loss or victory. I find that I rather can't, and probably should stop trying.
To provide a perhaps inappropriate analogy from the field of medicine & food... if a person has a weak immune system, 25 cells of tuberculosis may start a runaway process leading to premature dealth. However, if a person is in good health, and the cells involved are instead a benign strain of lactobacillus, a person may well drink a few billion of them, in the form of a cup of yoghurt, and not suffer in health but gain more.
EDIT: sorry, edited a dozen times to finally express a close approximation to what I ought really mean. :D